EUROPEAN COOPERATION

IN THE FIELD OF SCIENTIFIC

AND TECHNICAL RESEARCH

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EURO-COST

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IC1004 TD(14) 09073

Ferrara, Italy

5-7 February, 2014

SOURCE: Jagiellonian University,

POLAND

Department of Telecommunications,

AGH University of Science and Technology,

POLAND

Communication in nano-scale via FRET

Krzysztof Wójcik, Kamil Solarczyk Jagiellonian University

Ul. Gołębia 24

31-007 Krakow

POLAND

Email: krzysztof.wojcik@uj.edu.pl, kamil.solarczyk@gmail.com

Pawel Kulakowski

Department of Telecommunications

AGH University of Science and Technology

Al. Mickiewicza 30

30-059 Krakow

POLAND

Phone: +48 12 617 3967

Email: kulakowski@kt.agh.edu.pl

Communication in nano-scale via FRET

Krzysztof Wojcik, Jagiellonian University

Kamil Solarczyk, Jagiellonian University

Pawel Kulakowski, AGH University of Science and Technology

ABSTRACT Nano-communication has gained significant attention in the last few years, as a means to

establish information transfer between future nano-machines. Comparing with other

communication techniques for nano-scale (calcium ions signalling, molecular or catalytic

nanomotors, pheromones propagation, bacteria-based communication), the phenomenon

called FRET (Förster Resonance Energy Transfer) offers significantly smaller propagation

delays and high channel throughput. In this paper, we report our recent experiments on FRET-

based nano-networks performed in the Laboratory of Cell Biophysics of the Jagiellonian

University, Kraków. We propose to use Alexa Fluor dyes as nano transmitters and receivers,

as they enable to create MIMO-FRET communication channels and thus enhance the FRET

efficiency. We measure FRET efficiency values, calculate the BER for the measured

scenarios and extend the calculations to consider a general case of MIMO (n,m) FRET

channels.

I. INTRODUCTION

Nano-machines are envisioned to be artificial mechanical devices that rely on nanometer

scale components. They are predicted to be basic building blocks for future nano-robots and

nano-processors [Akyildiz-2008, Suda-2005]. Their existence will create the possibility to

manipulate the animate and inanimate matter on a very low level. They promise an enormous

spectrum of applications: from biomedical (genetic engineering, health monitoring, medicines

delivery) and industrial (material fabrication) to environmental ones (pollution removing,

control over nature ecosystems). Because of its low complexity and size, the possible tasks

taken by nano-machines are very limited. In order to perform more complicated operations,

these devices must cooperate together, working as large well-organised structures, i.e.

constituting networks. Hence, the crucial issue is to enable efficient communication between

nano-devices.

The current progress in the area of nano-technology spurred the development of its younger

sister: nano-communications. A large number of nano- and micro-scale mechanisms was

recently analysed from the communication view-point: calcium ions signalling [Nakano-

2005], flagellated bacteria carrying DNA-coded information [Gregori-2010], molecular

motors [Moore-2006, Serreli-2007], pheromones and pollen propagation [Parcerisa-2009] and

others [Nakano-2013]. Most of them, however, guarantee neither a good throughput nor an

acceptably low transmission delay.

Here, we consider the phenomenon of Förster Resonance Energy Transfer (FRET) as a means

for efficient nano-communication. It is a spectroscopic process in which one molecule

transfers its excitation energy non-radiatively over a distance of 1-10 nm to another molecule

[Forster-1948]. The FRET phenomenon has some critical communication advantages. The

first one is a very short timescale of the energy transfer that occurs in nanoseconds. Second,

the FRET probability depends on the matching between the emission and absorption spectra

of the molecules and decreases with the sixth power of the distance between them.

Consequently, FRET can be simultaneously used in different parts of a nano-network, like a

wireless spectrum band in a cellular network.

Nano-communication via FRET was already discussed in [Kuscu-2012, Kuscu-2013] where

information theory analysis and simulation results for FRET channels were given. In this

paper, we present experimental results of FRET-based communication in nano-networks of

antibodies (Immunoglobulin G) labelled with Alexa Fluor (AF) fluorescent dyes. Antibodies

have the ability to recognise some parts of specific molecules and thus they can be thought of

as nano-machines (more specifically: nano-sensors), while AF dyes act as their nano-

transceivers transmitting and receiving information bits encoded in quanta of excitation

energy. We propose to use AF dyes, as they enable multiple-input multiple-output (MIMO)

FRET communication. We give the measured FRET efficiencies, calculate bit error rates for

the measured scenarios and extend the calculations to consider a general case of MIMO (n,m)

FRET channels. The main contribution of this paper can be listed as following:

• a FRET nano-scale MIMO communication technique based on AF dyes is proposed,

• experimental results of FRET efficiencies for AF-based FRET networks are shown,

• bit error rates for MIMO (n,m) FRET channels are calculated.

The rest of the paper contains the following sections. In Section II, the FRET theory and the

feasibility of FRET multi-hop communication are considered. In Section III, the details are

given on constructing the AF-based FRET networks. Next two sections contain the

description of the laboratory methodology and the obtained measurement results. The bit error

rate calculations for MIMO (n,m) FRET channels are presented and illustrated in Section VI

and finally the paper is concluded in Section VII.

II. FÖRSTER RESONANCE ENERGY TRANSFER

Förster Resonance Energy Transfer1 (FRET) is an energy process involving two molecules.

The first one, called donor, should be in the excited state, e.g. after absorbing a photon. The

second molecule is called acceptor and should be in the ground state. The energy is

transferred from the donor to the acceptor (usually 1-10 nm) non-radiatively, without an

emission of any photon, by the long range dipole-dipole interaction of both molecules (the

explanation of FRET assumes that both molecules are dipoles oscillating with similar

frequencies that can exchange energy with each other [Lakowicz-2006]). The rate of the

energy transfer and the range of distances over which it can be observed depend mainly on the

overlap of the donor emission spectrum and the acceptor absorption spectrum for a given

donor-acceptor pair. These relationships were first measured by Förster [Forster-1948], and

later studied by Stryer and colleagues [Stryer-1978].

If the donor molecule is excited not by an external photon, but the energy comes from a

chemical reaction, the phenomenon is called Bioluminescence Resonance Energy Transfer

(BRET). BRET has some advantages over FRET. First, the excitation of the donor

1 The abbreviation FRET is sometimes resolved as Fluorescence Resonance Energy Transfer, which however

seems to be a misconception, as the phenomenon does require neither a donor nor an acceptor to be fluorescent.

Because of that reason, some authors just use the name Resonance Energy Transfer abbreviated as RET. Here,

we follow the most common norm, where 'F' in FRET stands for Förster, honouring Theodor Förster (1910-

1974), the author of the RET theory.

fluorophore in FRET may also lead to the simultaneous excitation of a small part of acceptor

fluorophores, which is obviously not desirable. Second, this excitatory light causes

photobleaching2 of the donor. Third, BRET signal to noise ratio is higher than FRET, thus

fewer molecules are needed to reach the same signal level.

II.A. FRET rate and efficiency

Let’s assume first that an excited molecule exists, but there is no other molecule (potential

acceptor) nearby. Then, the energy of the molecule is usually released by a photon emission.

It can be also dissipated by other non-radiative mechanisms like quenching or decay processes

(Fig. 1).

Fig. 1. The simplified Jablonski diagram showing possible energy transitions in an excited molecule.

The time a molecule spends in the excited state before returning to its ground state is called

the lifetime of the excited state of the molecule. The average lifetime of the molecule in the

absence of FRET transfer can be calculated as the inverse of the sum of its emission rate eµ

and its rate of non-radiative decay mechanisms (i.e. quenching or non-radiative relaxation)

nrµ :

nre

FRETno µµτ

+=−

1. (1)

The emission and the non-radiative decay are random processes with exponential

distributions.

It should be noted that some energy is usually lost in the molecule between excitation and

emission due to rapid decays between vibrational energy levels (see Fig. 1). The resulting

difference between the molecule absorption and emission spectra is called the Stokes shift3.

Now, if another molecule, being in the ground state, exists in the vicinity of the excited one,

the excitation energy can be also released by FRET. In order to have it happen, two conditions

must be met. First, both molecules must be in the distance of 1-10 nm from each other.

Second, the emission spectrum of the excited molecule, called donor, must overlap the

2 Photobleaching is a phenomenon of chemical modification of the fluorophore, which in turn loses its ability to

emit photons. This is usually caused by breaking open or bonding of the fluorophore to nearby molecules.

Although photobleaching is generally assumed to be irreversible, in some cases the fluorophore can be switched

on again after loss of emission ability.

3 For Sir George Gabriel Stokes (1819-1903), who was the first to observe this phenomenon in 1852.

absorption spectrum of the ground state molecule, called acceptor. The FRET rate can be

calculated as [Lakowicz-2006]:

∫∞

⋅⋅⋅⋅⋅⋅

⋅⋅

⋅=

0

4

456

2

)()(128

10ln9000λλλελ

πκµ

µ ddFnNr

AD

e

FRET (2)

The term eµ is for the donor emission rate and r is the distance between the molecules. The

factor 2κ is responsible for the relative orientation between the donor and acceptor dipoles

and is usually assumed to be 32 which is suitable when both molecules can move by

rotational diffusion [Lakowicz-2006], which is also the case of the experiments reported here.

The term N is the Avogadro number, n is the refractive index assumed to be equal to 1.4 for

the biomolecules in aqueous solutions. Finally the integral part of the equation is responsible

for the molecules spectra overlap: )(λDF is the normalised emission spectrum of the donor,

)(λε A is the absorption spectrum of the acceptor. As the FRET rate depends on the sixth

power of r , the phenomenon is commonly used in spectroscopy for very accurate

measurements of distances between molecules.

With an acceptor nearby, FRET is another possibility for the donor molecule to dissipate its

energy. In general, there can be more that one neighbouring molecule in the vicinity of the

donor and each of them can be the acceptor in the FRET transfer. All these neighbouring

molecules contribute to the total FRET rate. Thus, comparing with (1), the donor average

lifetime decreases and is equal to:

∑=

++=

k

iiFRETnre

FRET

1,

1

µµµτ , (3)

where iFRET ,µ is the FRET rate of the th−i possible acceptor among k ones. Knowing eµ ,

nrµ and all iFRET ,µ rates, we can also calculate the FRET efficiency iE , i.e. the fraction of

the excited donors that decay through FRET to the th−i acceptor [Lakowicz-2006]:

∑=

++=

k

iiFRETnre

iFRET

iE

1,

,

µµµ

µ. (4)

The FRET efficiency iE is also the probability that the energy is transferred to the th−i

acceptor. Thus, the total probability that the energy is transferred to any of the acceptors is

given by:

∑

∑

=

=

++=

k

iiFRETnre

k

iiFRET

E

1,

1,

µµµ

µ. (5)

The distance between the donor and the acceptor where nreFRET µµµ += is called the Förster

distance 0R , which can be measured or calculated with (2), for each donor-acceptor pair.

Knowing 0R , the FRET rate can be obtained from a simplified formula:

60 )()(r

RnreFRET ⋅+= µµµ . (6)

If there is only one possible acceptor (or others have negligibly small FRET rates), the FRET

efficiency can be calculated as:

60

6

60

Rr

RE

+= , (7)

what means that for 0Rr = , %50=E and FRETnoFRET −⋅= ττ 21 .

If there are many acceptors, the FRET efficiency is given by:

∑

∑

=

=

⋅+

⋅

=k

i i

k

i i

rR

rR

E

16

60

16

60

11

1

, (8)

where ir is the distance from the donor to the th−i acceptor. If the acceptors are equally

distant from the donor, (8) simplifies to:

60

6

60

Rkr

RkE

⋅+

⋅= . (9)

In practice, neither FRET rate nor its efficiency could be measured directly. FRET used to be

measured by observing changes in donor's and acceptor's fluorescence intensities. These

intensity-based methods, however, have a major drawback due to the influence of

photobleaching on measured FRET efficiencies. The alternative, more reliable method of

measuring FRET is based on fluorescence lifetimes. What can be observed in this kind of

measurements is the decrease of the average lifetime of the donor molecule after the acceptor

is added. Having FRETno−τ and FRETτ values and applying (1) and (3) to (4), we obtain:

FRETno

FRET

FRET

FRETnoFRETE−

−

−−

−

−=−

=ττ

τ

ττ1

1

11

. (10)

II.B. FRET time scale and throughput

Comparing with different nano-scale communication mechanisms, FRET occurs much faster.

The whole process can be divided into three phases. First, a donor molecule absorbs a photon

which takes less than a femtosecond ( 1510− s). Then, the excess of energy is dissipated rapidly

by the internal conversion to the lowest vibrational energy level 1S , which occurs in about a

picosecond ( 1210− s). After that, the FRET occurs after a random delay equal to the donor

excited state lifetime which is of order of nanoseconds. Finally, the donor molecule is again in

the ground state, while the acceptor is excited. Summing up the three phases, the delay of the

whole energy transfer is of order of nanoseconds. Assuming that a single information bit is

going to be sent each time (e.g. '1': the donor is excited, '0': no excitation), the FRET channel

throughput can be estimated as tens of Mbits/s.

II.C. Multi-hop FRET communication

The FRET phenomenon can occur between any types of spectrally matched molecules, see

(2). They can be of biological origin, i.e. organic molecules, or artificial ones, e.g. quantum

dots. In biophysics, it is very common to observe FRET for fluorophores, i.e. organic

molecules which emission spectra cover the range of visible light. For the purpose of

communication via FRET, the molecules emission/absorption spectra can be also located in

other parts of the electromagnetic spectrum, e.g. ultraviolet or infrared bands.

It is worth to note that the FRET phenomenon can be used for multi-hop transmissions in

molecule chains, where two of more energy transfers occur, one by one. In such a scenario,

the acceptor in the first FRET pair is at the same time the donor in the second pair, allowing

the signal to pass two or more hops (see Fig. 2a). Because of the Stokes shift, some energy is

wasted in each hop and the absorption spectrum for the second acceptor lies in the longer

wavelengths (lower frequencies) range that for the first acceptor (Fig. 2b). It means that

FRET channels are in general one-directional4: in Fig. 2a, the transfer A→ B → C is feasible,

but C → B → A is very unlikely. As the FRET rate decreases with the sixth power of the

distance, it is generally more efficient to transfer a signal via multi-hop FRET than directly.

One must assure, however, that all the FRET efficiencies are high enough. The total transfer

efficiency is the product of the FRET efficiencies for all the hops. FRET efficiencies in a

multi-hop transfer are independent of each other. It is confirmed by the Kasha's rule stating

that the emission spectrum of a molecule does not depend on its excitation wavelength

[Kasha-1950].

Fig. 2. a. An example of a chain of molecules where multiple FRET reactions can occur.

b. Respective emission and absorption spectra of A, B and C molecules.

III. FRET NETWORKS

The current level of nanotechnology does not allow us to create networks of nano-machines

freely moving, approaching each other and communicating. Instead, with the aid of

biotechnology techniques, we can construct structures made of proteins, potential nano-

machines, and attach to them some fluorophores which can communicate via FRET with each

other. It means that we cannot create any network structure, but we are rather limited by the

geometry of the available proteins.

4 There are some exceptions, see the homotransfer phenomenon which occurs e.g. between Bodipy fluorophores

[Lakowicz-2006] or YO-PRO-1 molecules [Hannestad-2008].

For the purpose of our studies, we built a FRET network composed of 3 antibodies (we used

Immunoglobulin G) labelled with fluorescent Alexa Fluor dyes. Antibodies are proteins that

have the ability to recognise some parts of specific molecules, thus they can be treated as

nano-sensors. The Alexa Fluor (AF) dyes are a family of fluorophores characterised by a good

robustness against photobleaching. Each fluorophore in the family is usually called Alexa

Fluor X, where X is the main wavelength, in nanometers, of its absorption spectrum. The AF

dyes can be easily labelled (attached) to antibodies, i.e. proteins of ca. 10-15 nm large. Thus,

fluorescent AF dyes can be considered as nano-FRET-transceivers attached to antibodies

working as nano-machines (nano-sensors).

While there are other components that can be used in FRET networking (see the summary at

the end of this section), we decided to choose the Alexa Fluor dyes mainly for their labelling

properties. Using these molecules, each antibody can be labelled not only with a single AF

dye, but with a large number of them (theoretically up to 10 dyes), depending on the degree of

labelling (DoL). In the result, we had a kind of multi-input multiple-output (MIMO) FRET

links between the antibodies. As explained in Section VI, having many AF dyes at both sides

of each link greatly increased the efficiency of the information transfer.

Our FRET network under study was constructed as follows. The first element of the network

was a histone H1 bound to a DNA molecule. Next, a primary antibody Ab0 was attached to

the histone H1. Then, Ab1, Ab2 and Ab3 antibodies were subsequently added (Ab2 and Ab3

were together attached to Ab1) in order to form the whole FRET network. Each of these 3

antibodies had been already labelled with AF dyes (see Fig. 3).

In general, antibodies allow building practically infinite chains, but the distances between

them cannot be controlled precisely. Our experiments were performed on HeLa 21-4 cells (a

common laboratory cell line derived from a human ovarian cancer) containing about 107 of

these histone H1 molecules in their nuclei. In the laboratory process of immunostaining, about

30–50% of histones are labelled with antibodies, thus we were able to create about 61053 ⋅−

similar fluorophore networks, which we assumed was a good statistical sample.

The main aim of our experiments was to measure the efficiency of the information transfer in

all the three communication links created between the antibodies: Ab1-Ab2, Ab2-Ab3 and

Ab1-Ab3. Each used antibody (Immunoglobulin G) had a shape of a 3-element airscrew [Tan-

2008] with a radius of ca. 7 nm (see Fig. 3). The distances between the antibodies Ab1-Ab2

and Ab1-Ab3 were about 9-12 nm, while Ab2-Ab3 distance is smaller, about 7-8 nm. The

antibodies Ab1, Ab2 and Ab3 were labelled with Alexa Fluor 405, 488 and 546 dyes,

respectively. AF dyes are rather small molecules, about 1.4-1.8 nm large. We used AF dyes

produced by Molecular Probes, Inc., having the following degrees of labelling:

• for AF 405, DoL = 2,

• for AF 488, DoL = 7,

• for AF 546, DoL = 4.

Due to the chemical properties of antibodies, the AF dyes always attach to their upper

elements. The exact position of the dyes on antibodies is, however, hard to determine. The

upper element of each antibody is about 7 nm long. Moreover, the dyes surround these

elements. As the result, the distances between the AF dyes may vary significantly. We can

estimate them as:

• AF 405 – AF 488 distances = 7-14 nm,

• AF 488 – AF 546 distances = 6-12 nm,

• AF 405 – AF 546 distances = 7-14 nm.

Fig. 3. The network of antibodies (Immunoglobulin G) and AF dyes used in the experiments.

The absorption and emission spectra of the AF dyes are shown in Fig. 4. The Förster distance

0R between AF488 and AF546 is equal to 6.4 nm [Lifetechnologies-1]; the 0R values for

AF405→AF488 and AF405→AF546 FRET transfers are, to the best of authors’ knowledge,

not published. The energy transfers in the opposite directions can be neglected as highly

unlikely, what can be confirmed with Fig. 4, as the respective emission and absorption spectra

do not match. It means that all the three communication links are unidirectional.

Fig. 4. Absorption (dashed lines) and emission (shaded areas) spectra of Alexa Fluor dyes [Lifetechnologies-2].

IV. LABORATORY METHODOLOGY

Since it is impossible to record the time decay profile of the signal from a single excitation-

emission cycle, fluorescence lifetimes were measured in the Time Correlated Single Photon

Counting (TCSPC) mode. This method is based on an accurate measurement of the time

between the excitation pulse and the arrival of the first photon to the SPAD (Single Photon

Avalanche Diode) detector. Numerous repetitions of this measurement permit to build a

histogram, which represents the time decay of the signal. Fitting the resulting histogram with

an exponential curve allows extracting the lifetime of a fluorophore.

FLIM (Fluorescence Lifetime Imaging Microscopy) measurements were done using a Leica

TCS SP5 II SMD confocal system integrated with FCS/FLIM TCSPC module (Fig. 5). This

module consists of picosecond laser diode heads (excitation at 405, 470 or 640 nm), coupled

to a laser driver (PDL 828 “Sepia II”), two SPAD detectors (PDM Series), a TCSPC module

(PicoHarp 300) and a detector router (PHR 800). In a typical measurement, a FLIM image

was acquired at 256x256 pixel resolution and at a speed of 200 lines/s. The acquisition time

for each image was one minute, with the laser power set to achieve a photon counting rate of

200-300 kCounts/s (the detection efficiency was about 1-10%). The fluorophores, AF405 and

AF488, were excited at a 20 MHz pulse repetition rate with 405 and 470 nm laser lines and

the emission was collected with 460-500 and 500-550 band-pass filters, respectively.

It is worth to notice that during each laser pulse, not more than few donor AF dyes were

excited among millions of them in our HeLa cells. Consequently, we could neglect the

situations with 2 or more excited dyes attached to the same antibody, what is important for the

later considerations on MIMO-FRET efficiency (see Section VI).

Fig. 5. Schematic representation of the Laser Scanning Microscope (LSM) integrated with a FLIM module. The

experiment begins when the sample is excited with a pulsed laser, which is controlled by a laser driver. This unit

permits to control the laser power output and its repetition rate. Upon excitation, the sample emits fluorescence

photons which are detected in SPAD detectors. In order to determine the exact time between the excitation pulse

and arrival of the first photon to the detector, a TCSPC module connected to a computer receives information

from the detectors, laser driver and laser scanner. In steady-state measurements (image acquisition without

information about fluorescence lifetimes), the sample is excited with a CW (continuous wave) laser, signal is

detected in PMT detectors and the resulting image is viewed on a LSM computer.

In each measurement a region of approximately 50x50 µm containing 2-4 cells was chosen. In

a given region three lifetime images were collected for AF405: one before and after each

staining with secondary antibodies Ab2 and Ab3 (tagged with AF488 and AF546

respectively), while for AF488 two lifetime images were collected: one before and one after

staining with AF546-tagged secondary antibody. Before analysis, to exclude the signal

resulting from non-specific staining, only the nuclei of cells were chosen. Due to possible

differences in the distance between attached antibodies resulting from chromatin compaction,

mitotic chromosomes were not analysed (see Fig. 6 A-F). The analysis was done in

SymPhoTime II software (PicoQuant GmbH) using tail fitting, excluding the IRF (Instrument

Response Function) time range. To improve signal to noise ratio, all nuclei in a given region

were analysed together, resulting in one decay for each image. Both AF405 and AF488

decays were fitted with a two-exponential function:

21 /2

/1)( ττ tt eAeAtF −− ⋅+⋅= (11)

where τ1 and τ2 are the lifetimes, while A1 and A2 represent the amplitudes of the components.

The goodness-of-fit was estimated based on the weighted residuals and the chi squared value.

For FRET efficiency calculations, see (10), the amplitude-weighted average lifetime was

used:

∑

∑ ⋅=

i

i

i

ii

A

A ττ (12)

The images of the observed cells (see Fig. 6) were obtained with a Leica TCS SP5 II SMD

confocal system (Leica Microsystems GmbH), equipped with a 63x NA 1.4 oil immersion

lens. Images (8 bit) were acquired at 512x512 pixel resolution, at a speed of 200 lines/s, with

1-3 frames averaged. For AF405 excitation, a 405 nm pulsed laser line was used, while Alexa

Fluor 488 and 546 were excited with 480 and 543 nm lines (Ar and HeNe lasers).

Fluorescence emission was collected using photomultipliers at 460-500, 500-550 and 580-630

nm, respectively. For the comparison of images before and after staining with secondary

antibodies, the same laser power and photomultiplier gain was used.

V. MEASUREMENT RESULTS

As explained in Section II.A, the FRET efficiency cannot be observed directly, i.e. measuring

the FRET rate. Instead, the lifetime of the excited state of the donor molecules is compared in

two scenarios: without and with the acceptor molecules, see (10).

It should be emphasized that, unlike the FRET efficiency, fluorescence life time of a dye

depends on pH, ion concentration and presence of other molecules in the solution. Thus, both

lifetime measurements, without and with the acceptor molecules, should be performed in the

same environment. Having this in mind, we always measured both fluorescent lifetimes on

the same selected population of molecules: there were 2-4 cell nuclei (see Fig. 6), each

contained ca. 3-5 x 106

FRET networks.

FLIM (Fluorescence Lifetime Imaging Microscopy) measurements showed the following

FRET efficiencies:

donor acceptor FRETno−τ [ns] FRETτ [ns] E [%]

AF 405 AF 488 4.91 4.20 14 AF 488 AF 546 3.26 1.75 46 AF 405 AF 546 3.08 2.79 9

Tab. 1. The results of the performed FLIM measurements

Additionally, FRET can be observed visually on confocal images by the decrease of the donor

fluorescence intensity in the presence of the acceptor, as shown in Fig. 6.

Fig. 6. The decrease of the fluorescence signal as a result of FRET transfers: AF 405 → AF 488, AF 488 → AF

546 and AF 405 → AF 546. HeLa cells were fixed and incubated with a primary antibody against histone H1.

Subsequently, the cells were stained with secondary antibodies (AF 405, 488 and 546) and images were

collected before and after staining with each antibody. A) A405 fluorescence before staining with A488. B)

A405 fluorescence after staining with A488. C) A488 fluorescence before staining with A546. D) A488

fluorescence after staining with A546. E) A546 fluorescence in cells previously stained with A405 and A488. F)

Transmitted light image of the cells showed in A-E. G) A405 fluorescence before staining with A405. H) A405

fluorescence after staining with A546. I) A546 fluorescence in cells previously stained with A405. J)

Transmitted light image of the cells showed in G-I.

FLIM measurements and confocal images confirm that the FRET transfer occurred in all three

communication links. As we do not know the exact distances between the AF dyes, it is hard

to verify if the measurement results match the FRET theory. Anyway, we can try to do that

for the FRET AF488→AF546, as we know the respective Förster distance: nm 4.60 =F . In

this link, for each donor we have 4 acceptors (for AF 546, DoL = 4). Assuming that each of

these 4 acceptors is located at the same distance r from the donor, we can put the measured

FRET efficiency and the Förster distance into the equation (9) and calculate: nm 3.8=r . The

calculated value matches our expectations: in Section III, the average distance between AF

488 and AF 546 dyes was estimated as 6-12 nm.

VI. MIMO-FRET CHANNELS

The FRET efficiency measured for all three communication links seems far from being

acceptable for telecommunication purposes. Let us adopt, like in [Kuscu-2012], the simple

ON-OFF keying modulation scheme. We can transmit a single bit '1' – exciting the donor and

hoping the energy is transferred via FRET to the acceptor – or a bit '0' – keeping the donor in

the ground state, i.e. not exciting it. Assuming no other source of excitation and no other

donors in the vicinity, transmission of '0' is always successful and transmission of '1' is

erroneous with the probability E−1 . If zeros and ones are equally probable to be transmitted,

the channel bit error rate (BER) is equal to ( )E−⋅ 15.0 , what means that even in the best

measured case (AF488→AF546) the BER is very high: 27%.

Obviously, the channel BER can be decreased by repeating each information bit numerous

times, at the cost of the channel capacity. Another possibility is to exploit multiple AF dyes at

both sides of each communication link. As stated in Section IV.A, in the performed

experiments we had only one donor AF dye excited at the same time. If more donor dyes

(attached to the same antibody) are excited, there is larger probability that at least one of them

transfers the excitation energy via FRET to the donor side. Thus, we can transmit '1' by

exciting as many donor dyes as possible. Then, the correct reception takes place when at least

one acceptor dye receives the energy via FRET. Transmission of '0' is realised as previously,

i.e. not exiting any donor. By using multiple dyes at both sides of the link we fully exploit the

multiple-input multiple-output (MIMO) character of the communication channel between the

AF dyes.

Let us assume that the FRET efficiency E in the ( )m,1 communication channel is equal

independently which donor AF dye is excited. In fact, what we have measured is the FRET

efficiency for different donor AF dyes averaged over tens of millions of excitation events5.

We can now give the probability of the correct reception of a bit '1' in the ( )mn,

communication channel which is the probability that at least one donor AF dye transfers its

excitation energy to an acceptor dye:

( )nEP −−= 11 . (13)

Consequently, the bit error rate for the ( )mn, channel is equal to:

( )nmn E−⋅= 15.0BER , , (14)

5 The photon counting rate at the detector was at least 200 kCounts/s, each experiment lasted not less than 1

minute and the maximum detector efficiency was 10%, thus we had at least 120x106 photons emitted. The FRET

efficiency was at least 6% what means we had at least 127x106 excitation events.

where E is the FRET efficiency for ( )m,1 communication channel measured experimentally

or calculated with (5) or (8). Therefore, we can calculate the mn,BER values for all three

communication links. These are the expected bit error rates in the case when all donor AF

dyes are excited each time a bit '1' is to be sent through the communication channel. The

mn,BER values are given in Table 2, together with measured FRET efficiencies.

donor donor

DoL acceptor

acceptor

DoL

MIMO channel

dimensions

E for (1,m)

channel

BER for

(n,m) channel

AF 405 2 AF 488 7 (2,7) 14 % 37 % AF 488 7 AF 546 4 (7,4) 46 % 0.7 % AF 405 2 AF 546 4 (2,4) 9 % 41 %

Tab. 2. Summary of measured FRET efficiencies and calculated BER values

We can see that the link AF488→AF546 is clearly the best and the only one with the

satisfactory BER value. On the one hand, it is the result of a bit smaller separation between

the donor and acceptor molecules: they are on average 1-2 nm closer than in other two links.

Such a difference can be crucial, as the FRET rate decreases with the sixth power of the

donor-acceptor separation, see again (2). On the other hand, it is the large number of Alexa

Fluor dyes at both donor and acceptor sides (11 in total) that enables to reduce the channel

BER. As a reference, we also calculated mn,BER values for some theoretical cases: donor and

acceptor DoL varying from 1 to 10 and donor-acceptor separation from 05.0 F to 07.1 F (see

Fig. 7). We can see that BER values are increasing rapidly with donor-acceptor distances. The

acceptable BER (about 1%) can be obtained even for large distances ( 05.1 Fr > ), but at the

cost of huge number of AF dyes involved. It also seems better to have balanced distribution of

dyes at both sides of the link, or a slightly more dyes at donor side than at acceptor side

(compare e.g. (4,4), (2,6) and (6,2) cases).

Fig. 7. Theoretical BER values for (n,m) MIMO-FRET channels

VII. CONCLUSIONS

In this paper, we discuss MIMO communication in nano-networks realised via FRET. We

propose to use Alexa Fluor dyes as nano transmitters and receivers. These molecules, having

degrees of labelling up to 10, can attach in large numbers to proteins working as nano-

machines and thus create reliable MIMO-FRET communication channels. We present

experimental results of FRET efficiencies for nano-networks of Immunoglobulin G proteins

labelled with Alexa Fluor 405, 488 and 546 dyes. We calculate bit error rates for the FRET

communication channels under study. Finally, we extend the calculations for a general case of

MIMO (n,m) FRET channels. We show that FRET communication can be reliable even on

ranges larger than the Förster distances if multiple fluorophores are involved at both sides of

the channel.

REFERENCES

[Akyildiz-2008] I.F. Akyildiz, F. Brunetti, C. Blazquez, "NanoNetworking: A New

Communication Paradigm", Computer Networks (Elsevier) Journal, vol. 52, pp. 2260-2279,

August, 2008.

[Suda-2005] T. Suda, M. Moore, T. Nakano, R. Egashira, A. Enomoto, "Exploratory research

on molecular communication between nanomachines", Proceedings of Genetic and

Evolutionary Computation Conference (GECCO’05), June 2005.

[Nakano-2005] T. Nakano, T. Suda, M. Moore, R. Egashira, A. Enomoto, K. Arima,

Molecular communication for nanomachines using intercellular calcium signaling,

Proceedings of the Fifth IEEE Conference on Nanotechnology, June 2005, pp. 478–481.

[Gregori-2010] M. Gregori, I.F. Akyildiz, "A New NanoNetwork Architecture using

Flagellated Bacteria and Catalytic Nanomotors," IEEE Journal of Selected Areas in

Communications, vol. 28, pp. 612-619, May 2010.

[Moore-2006] M. Moore, A. Enomoto, T. Nakano, R. Egashira, T. Suda, A. Kayasuga,

H. Kojima, H. Sakakibara, K. Oiwa, "A design of a molecular communication system for

nanomachines using molecular motors", Proceedings of the Fourth Annual IEEE

International Conference on Pervasive Computing and Communications (PerCom’06), March

2006.

[Serreli-2007] V. Serreli, C. Lee, E.R. Kay, D.A. Leigh, A molecular information ratchet,

Nature 445: 523–527, 2007.

[Parcerisa-2009] L. Parcerisa, I.F. Akyildiz, "Molecular Communication Options for Long

Range Nanonetworks", Computer Networks (Elsevier) Journal, vol. 53, pp. 2753-2766, 2009.

[Nakano-2013] Tadashi Nakano, Andrew W. Eckford, Tokuko Haraguchi "Molecular

Communications", Cambridge University Press, 2013.

[Forster-1948] T. Förster "Zwischenmolekulare Energiewanderung und Fluoreszenz",

Annalen der Physik, vol. 437, no. 1–2, pp. 55–75, 1948.

[Kuscu-2012] M. Kuscu, O.B. Akan "A Physical Channel Model and Analysis for Nanoscale

Communications with Förster Resonance Energy Transfer (FRET),"IEEE Transactions on

Nanotechnology, vol. 11, no. 1, pp. 200-207, January 2012.

[Kuscu-2013] M. Kuscu, O.B. Akan "Multi-Step FRET-Based Long-Range Nanoscale

Communication Channel", IEEE Journal on Selected Areas in Communications (JSAC), vol.

31, no. 12, pp. 715-725, December 2013.

[Lakowicz-2006] Joseph R. Lakowicz "Principles of Fluorescence Spectroscopy 3 ed.",

Springer, 2006.

[Stryer-1978] L. Stryer "Fluorescence energy transfer as a spectroscopic ruler", Annual

Review of Biochemistry, vol. 47, pp. 819–846, 1978.

[Hannestad-2008] Jonas K. Hannestad, Peter Sandin, Bo Albinsson "Self-Assembled DNA

Photonic Wire for Long-Range Energy Transfer", Journal of the American Chemical Society

130(47):15889-95, 2008.

[Kasha-1950] M. Kasha "Characterization of electronic transitions in complex molecules",

Discussions of the Faraday Society 9:14–19, 1950.

[Tan-2008] Yih Horng Tan, Maozi Liu, Birte Nolting, Joan G. Go, Jacquelyn Gervay-Hague,

Gang-yu Liu, "A Nanoengineering Approach for Investigation and Regulation of Protein

Immobilization", ACS Nano 2 (11), pp. 2374–2384, 2008.

[Lifetechnologies-1] http://www.lifetechnologies.com/pl/en/home/references/molecular-

probes-the-handbook/tables/r0-values-for-some-alexa-fluor-dyes.html

[Lifetechnologies-2] http://www.lifetechnologies.com/europe-other/en/home/life-science/cell-

analysis/labeling-chemistry/fluorescence-spectraviewer.html